an investigation of dual stator winding induction machines

There are two unknown variables in (2.8). One equation cannot solve two unknowns,
hence the stator yoke flux is chosen as the second objective function in this design. The
stator yoke flux corresponds to the integral of the air gap flux density, for the dual-
winding design:
∫
θ
[ ( θ ) − K cos(
3θ
+ δ ) ]
φ y = rlB cos dθ
(2.9)
2 / 6
2
0
1
1
where, r is the mean air gap radius and l is the stator core length. After the integration,
the stator yoke flux can be written as:
⎡ K1
⎤
φ y 2 / 6 = rlB ⎢sin(
θ ) − sin(
3θ
+ δ1
) ⎥⎦
(2.10)
⎣ 3
2
At the peak point of yoke flux, the derivative of φ y2
6 with respect to angle θ is
equal to zero, which can be expressed as:
φ
d y2
/ 6
dθ
[ ( θ ) − K cos(
3θ
+ ) ] = 0
cos 2
1
1
= rlB
δ
π
When θ = and 1 0
2
= δ , the peak value of the stator yoke flux can be found as:
51
(2.11)
⎛ K1
⎞
φ y2
/ 6 = rlB2⎜1
+ ⎟
(2.12)
⎝ 3 ⎠
The peak value of the flux in the yoke for the 4-pole machine can be written as:
rlB 4 φ y 4 =
(2.13)
2
To maintain the same level of saturation, the peak yoke flux value of the 2/6 pole
design and the 4-pole design should be the same, which can be expressed as:
⎛ K1
⎞ rlB 4
rlB 2⎜1
+ ⎟ =
(2.14)
⎝ 3 ⎠ 2